Statistical estimation and inference via local SGD in federated learning

作     者：Li, Xiang Liang, Jiadong Chang, Xiangyu Zhang, Zhihua 

作者机构：School of Mathematical Sciences Peking University China Center for Intelligent Decision-Making and Machine Learning School of Management Xi'an Jiaotong University China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2021年

核心收录：

主　　题：Iterative methods 

摘      要：Federated Learning (FL) makes a large amount of edge computing devices (e.g., mobile phones) jointly learn a global model without data sharing. In FL, data are generated in a decentralized manner with high heterogeneity. This paper studies how to perform statistical estimation and inference in the federated setting. We analyze the so-called Local SGD, a multi-round estimation procedure that uses intermittent communication to improve communication efficiency. We first establish a functional central limit theorem that shows the averaged iterates of Local SGD weakly converge to a rescaled Brownian motion. We next provide two iterative inference methods: the plug-in and the random scaling. Random scaling constructs an asymptotically pivotal statistic for inference by using the information along the whole Local SGD path. Both the methods are communication efficient and applicable to online data. Our theoretical and empirical results show that Local SGD simultaneously achieves both statistical efficiency and communication efficiency. Copyright © 2021, The Authors. All rights reserved.